Symbol n
n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Published equation contexts
Why this formula appears here
Compaction and editing are not free, and the model above shows why they earn their keep anyway. Reset the accumulated history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with , but the number of segments scales with n/m , so the total across the whole trajectory scales with m n — linear in n for a fixed segment length m , not quadratic. The summarization step itself is not free — reading through a full segment once to compress it costs roughly what one ordinary step near the end of that segment costs — so an interval m chosen too…
Read the representative guide
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (2)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 40 · AI Agents & Systems
The Economics and Physical Limits of Running AI Agents at Scale
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Compaction and editing are not free, and the model above shows why they earn their keep anyway. Reset the accumulated history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with , but the number of segments scales with n/m , so the total across the whole trajectory scales with m n — linear in n for a fixed segment length m , not quadratic. The summarization step itself is not free — reading through a full segment once to compress it costs roughly what one ordinary step near the end of that segment costs — so an interval m chosen too…
Meanings in this article
Equation guide → · Article →Equation 42 · AI Agents & Systems
The Economics and Physical Limits of Running AI Agents at Scale
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Compaction and editing are not free, and the model above shows why they earn their keep anyway. Reset the accumulated history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with , but the number of segments scales with n/m , so the total across the whole trajectory scales with m n — linear in n for a fixed segment length m , not quadratic. The summarization step itself is not free — reading through a full segment once to compress it costs roughly what one ordinary step near the end of that segment costs — so an interval m chosen too…